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# Two Way ANOVA: Gender, Marital Status, and Happiness

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Submit your answers to the following questions using the ANOVA source table below. The table depicts a two-way ANOVA in which gender has two groups (male and female), marital status has three groups (married, single never married, divorced), and the means refer to happiness scores (n = 100):

What is/are the independent variable(s)? What is/are the dependent variable(s)?
What would be an appropriate null hypothesis? Alternate hypothesis?
What are the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance?
Calculate the mean square for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance.
Calculate the F ratio for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
Identify the critical Fs at alpha = .05 for 1) gender, 2) marital status, and 3) interaction between gender and marital status.
If alpha is set at .05, what conclusions can you make?
Source Sum of Squares (degrees of freedom [df]) Mean Square Fobt. Fcrit.
Gender 68.15 ? ? ? ?
Marital Status 127.37 ? ? ? ?
Gender * Marital Status (A x B) 41.90 ? ? ? ?
Error (Within) 864.82 ? ? NA NA
Total 1102.24 99 NA NA NA

https://brainmass.com/statistics/analysis-of-variance/two-way-anova-gender-marital-status-and-happiness-535857

#### Solution Preview

What is/are the independent variable(s)? What is/are the dependent variable(s)?
Independent Variables: Gender and marital status
Dependent Variable: Happiness

What would be an appropriate null hypothesis? Alternate hypothesis?

Null Hypothesis: The population means of gender are equal to each other
Alternate hypothesis: The population means of each gender are not equal to each other

Null Hypothesis: The population means of marital status are equal to each other
Alternative Hypothesis: The population means of each marital status
Null Hypothesis: There is no interaction between gender and marital status
Alternative Hypothesis: There is an interaction between gender and marital status

What are the degrees of freedom for 1) gender, 2) marital status, 3) interaction between gender and marital status, and 4) error or within variance?

1. Gender: Since there are two types of gender, degrees of freedom of gender would be 2-1=1
2. Marital Status: Since there are three types of marital status, degrees of freedom of marital status would be 3-1=2
3. Interaction ...

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